Answer
$$(t-2)(t+1)^2=t^3-3t-2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(t-2)(t+1)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(t-2)(1t^2+2t+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}t^3+2t^2+t-2t^2-4t-2 \xlongequal{ } \\[1 em] & \xlongequal{ }t^3+ \cancel{2t^2}+t -\cancel{2t^2}-4t-2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}t^3-3t-2\end{aligned} $$ | |
| ① | Find $ \left(t+1\right)^2 $ using formula. $$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ t } $ and $ B = \color{red}{ 1 }$. $$ \begin{aligned}\left(t+1\right)^2 = \color{blue}{t^2} +2 \cdot t \cdot 1 + \color{red}{1^2} = t^2+2t+1\end{aligned} $$ |
| ② | Multiply each term of $ \left( \color{blue}{t-2}\right) $ by each term in $ \left( t^2+2t+1\right) $. $$ \left( \color{blue}{t-2}\right) \cdot \left( t^2+2t+1\right) = t^3+ \cancel{2t^2}+t -\cancel{2t^2}-4t-2 $$ |
| ③ | Combine like terms: $$ t^3+ \, \color{blue}{ \cancel{2t^2}} \,+ \color{green}{t} \, \color{blue}{ -\cancel{2t^2}} \, \color{green}{-4t} -2 = t^3 \color{green}{-3t} -2 $$ |
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